A stochastic switched SIRS epidemic model with nonlinear incidence and vaccination: Stationary distribution and extinction

In this paper, a stochastic epidemic system with both switching noise and white noise is proposed to research the dynamics of the diseases. Nonlinear incidence and vaccination strategies are also considered in the proposed model. By using the method of stochastic analysis, we point out the key parameters that determine the persistence and extinction of the diseases. Specifically, if [Formula: see text] is greater than 0, the stochastic system has a unique ergodic stationary distribution; while if [Formula: see text] is less than 0, the diseases will be extinct at an exponential rate.